Cosmological constant: a lesson from Bose-Einstein condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.     

Chaplygin gas quantum universe in the presence of the cosmological constant

We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant. We apply the Schutz’s variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the effective cosmological constant during the transition from the early times to the late times. For the case of an effective negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale factors never tend to the singular point, we have an initial indication that this model may not have singularities at the quantum level.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

Absence of preclassical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.     

Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations

We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is equivalent to the Robertson–Walker metric of cosmology. This general solution shows interconnections among many 5D solutions, such as the solution in the braneworld scenario and the topological black hole with cosmological constant. If the 5D cosmological constant is positive, the metric periodically depends on the extra dimension. Thus we can compactify the extra dimension on S¹${\mathrm{S}}^1$ and study the phenomenological issues. We also generalize the metric ansatz to the higher-dimensional case, in which the 4D part of the Einstein equations can be reduced to a linear equation.     

Friedmann cosmology with decaying vacuum density

Among the several proposals to solve the incompatibility between the observed small value of the cosmological constant and the huge value obtained by quantum field theories, we can find the idea of a decaying vacuum energy density, leading from high values at early times of universe evolution to the small value observed nowadays. In this paper we consider a variation law for the vacuum density recently proposed by Schützhold on the basis of quantum field estimations in the curved, expanding background, characterized by a vacuum density proportional to the Hubble parameter. We show that, in the context of an isotropic and homogeneous, spatially flat model, the corresponding solutions retain the well established features of the standard cosmology, and, in addition, are in accordance with the observed cosmological parameters. Our scenario presents an initial phase dominated by radiation, followed by a dust era long enough to permit structure formation, and by an epoch dominated by the cosmological term, which tends asymptotically to a de Sitter universe. Taking the matter density equals to half of the vacuum energy density, as suggested by observation, we obtain a universe age given by Ht = 1.1, and a decelerating parameter equals to −1/2.     

Two-Fluid Cosmological Model of Bianchi Type-V with Negative Constant Deceleration Parameter

This paper deals with a two-fluid Bianchi type-V anisotropic cosmological model with negative constant deceleration parameter. Exact solution of Einstein’s field equations for interacting matter and radiation field is presented which represents an expanding shearing and nonrotating cosmological model of the universe. This model describes the accelerated phase of the expanding universe. The physical and kinematical behaviors of the model are discussed.     

A generalized Heckmann–Schucking cosmological solution in the presence of a negative cosmological constant

An exact solution of the Einstein equations for a Bianchi-I universe in the presence of dust, stiff matter and a negative cosmological constant, generalising the well-known Heckmann–Schucking solution is presented. This solution describes a universe existing during a finite period of cosmic time, where the beginning and the end of its evolution are characterized by the presence of Kasner type cosmological singularities.     

What Can the Quantum Liquid Say on the Brane Black Hole, the Entropy of an Extremal Black Hole, and the Vacuum Energy?

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the near-extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon—the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum.     

Inflationary Cosmology with Two-component Fluid and Thermodynamics

We present a simple and self-consistent cosmology with a phenomenological model of quantum creation of radiation and matter due to the decay of the cosmological constant . The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation-dominated era, without reheating, and then evolves to the dust era. The initial vacuum for radiation and matter is a regular Minkowski vacuum. The created radiation and matter obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. This paper is an extension of the model with the decaying cosmological constant considered in [1]. We compare our model with the quantum field theory approach to creation of particles in curved space.     

Symmetry Breaking for Matter Coupled to Linearized Supergravity from the Perspective of the Current Supermultiplet

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.     

Gauss-Bonnet as Effective Cosmological Constant

It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant.We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions.Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter.One branch(the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero,in which case the effective cosmological constant becomes identical with the bare value,while the other(i.e.the "+") branch is singular in the same limit,and beyond this singular limit,the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.     

Quantization of closed mini-superspace models as bound states

The Wheeler-DeWitt equation is applied to closedk>0 Friedmann-Robertson-Walker metric with various combination of cosmological constant and matter (e.g., radiation or pressureless gas). It is shown that if the universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a nondegenerate bound state system, the eigen-wave functions are real (Hartle-Hawking). Furthermore, as a bound state problem, there exists a quantization condition that relates the curvature of the three space with the various energy densities of the universe. If we assume that our universe is closed, then the quantum number of our universe isN(Gk)^–110¹²². The largeness of this quantum number is naturally explained by an early inflationary phase which resulted in a flat universe we observe today. It is also shown that if there is a cosmological constant >0 in our universe that persists for all time, then the resulting Wheeler-DeWitt equation describes a non-bound state system, regardless of the magnitude of the cosmological constant. As a consequence, the wave functions are in general complex (Vilenkin).     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

Conformal Anomaly and Large-ScaleGravitational Coupling

We present a model in which the breakdown of conformal symmetry of a quantumstress-tensor due to the trace anomaly is related to a cosmological effect in agravitational model. This is done by characterizing the traceless part of thequantum stress-tensor in terms of the stress-tensor of a conformal invariantclassical scalar field. We introduce a conformal frame in which the anomaloustrace is identified with a cosmological constant. In this conformal frame weestablish the Einstein field equations by connecting the quantum stress-tensorwith the large-scale distribution of matter in the universe.     

Randall-Sundrum model for self-tuning the cosmological constant

The vanishing cosmological constant in the four-dimensional space-time is obtained in a 5D Randall-Sundrum model with a brane (B1) located at y = 0. The matter fields can be located at the brane. For settling any vacuum energy generated at the brane to zero, we need a three-index antisymmetric tensor field A(MNP) with a specific form for the Lagrangian. For the self-tuning mechanism, the bulk cosmological constant should be negative.     

Troubles with Quantum Anisotropic Cosmological Models: Loss of Unitarity

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schrödinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schrödinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.     

Vacuum energy and the universe in special relativity

The problem of the cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, vacuum energy is important for the Universe even in the absence of gravity, i.e., in the case when Newton’s constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity and find that, as in general relativity, the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G and thus is valid in the limit G→0. However, the result obtained for the vacuum energy in a world without gravity, i.e., when G=0 exactly, is different.     

The cosmic acceleration due to an alternative interpretation of the cosmological constant

In common discussions, the cosmological constant is identified with vacuum energy. The idea here is to identify it with the Lorentz-invariant scalar arisen by the contraction of the stress-energy tensor of ordinary matter which represents a form of the quintessence. We describe a quintessence cosmological scenario within the Friedmann universe and confront it with data.